question_answer

Construct a triangle ABC in which \[AB=5\text{ }cm,\text{ }BC=6\text{ }cm\] and \[\angle ABC=60{}^\circ \]. Now construct another triangle whose sides are \[\frac{5}{7}\] times the corresponding sides of \[\Delta \text{ }ABC\].

Answer:

Steps of construction:

(i) Draw a line segment \[AB=5\,\,cm\].

(ii) Construct \[\angle ABX=60{}^\circ \].

(iii) From B, draw \[BC=6\text{ }cm\] cutting BX at C

(iv) Join AC

Thus, \[\Delta \text{ }ABC\] is obtained

(v) Step 5: Draw D on AB such that \[AD=\frac{5}{7}AB\]\[=\left( \frac{5}{7}\times 5 \right)cm=3.6\,cm\]

(vi) Step 6: Draw \[DE||BC\] cutting AC at E. Then \[\Delta \text{ }ADE\] is the required triangle similar to \[\Delta \text{ }ABC\], such that each side of \[\Delta \text{ }ADE\]is \[\frac{5}{7}\] times the corresponding side of \[\Delta \text{ }ABC\].